The logic of quantum mechanics derived from classical general relativity
For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.
Key wordsgeons closed timelike curves quantum mechanics general relativity quantum logic
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- 6.K. S. Thorne, “Closed timelike curves” inProceedings, 13th International Conference on General Relativity and Gravity, 1992 (Institute of Physics Publishing, Bristol, 1992).Google Scholar
- 7.L. E. Ballentine,Quantum Mechanics (Prentice Hall, New Jersey, 1989).Google Scholar
- 8.P. R. Holland,The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).Google Scholar
- 9.P. A. Schilpp, ed.,Albert Einstein: Philosopher-Scientist (Cambridge University Press, Cambridge, 1970).Google Scholar
- 12.C. J. Isham, “Structural issues in quantum gravity,” plenary session lecture given at the GRG 14 Conference, Florence, grqc/9510063, August 1995.Google Scholar